# Treee

Treee is a language created by Octogeddonling (talk) 08:49, 4 January 2023 (UTC) . It replaces all letters in lambda calculus into trees of brackets and adds some mess to turn the entire code into uncomputable gibberish.

## Grammar

• call all the following an "operation"
• suppose the object have the form(another object...another object) and () is an object
• if the object has form(()followed by at least 3 objects), delete the outer bracket of second and third object, then replace every first object in the second object with the de-bracketed third object, than delete the first (), first object and third object's entirety.
• for example, (()()(()(()))(()()(()(())))) outputs itself.
• this step is edited 3 times to actually create a quine
• if the object has form(((()))followed by at least 1 object), delete the first 2 objects in the outermost bracket and prints a character whose ASCII code is equal to the total number of pair of brackets in the second object
• for example, (((()))(((((((((((((((((((((((((((((((())))))))))))))))))))))))))))))))) prints a space and outputs ()
• for any given number of spaces, just repeat the code above in the same trunk
• if the object has form(((()()))followed by at least 3 objects), then if an operation to the first input ultimately halts and returns a tree with no branches, then the first four is replaced by just the second, otherwise the third object.
• for example, ((()())A(()()(()(()))(()()(()(()))))(())) reverses the halt for A. This can be used to create a paradox but it's not computable anyway
• the form((()()())followed by at least 3 objects) works in a similar way but instead of checking the halting problem it will check any paradox in the first input. Replace the first four with the second if it's well-founded and return the third if it's not.
• repeat the 4 actions until nothing can be done
• scan all objects in this layer with an operation followed by an operation of this layer each time. For example if A turns into a, than the operation of (Abcd)operates(Abcd), then operates A, then operates (abcd), then operates b
• halt and output if really nothing can be done here

## Numeric Form

you can rewrite the whole code into numbers, such as (()()(()(()))(()()(()(())))) to 4 0 0 2 0 1 0 3 0 0 2 0 1 0. now you can write an interpreter of no action 3 and 4 using just Brainfuck!

## Version 2

• Version 2 is a simplification to the original one
• the fourth transformation is omitted
• let the transformation of (()A(B)(C)E) be:
• if A reduces to a tree without branch, aka () (()) ((()))..., the result would be (((B))E)
• else, the result will be (BC(C)E)
• if the operation above triggers a paradox, the result would be (((C))E)
• the trigger for printing is (()) now

## Version 3

• Version 3 is easier to understand and it is Turing complete anyway
• The form of an operation is (()(A)(B)(C)D), as it in version 1
• if (A) reduces to a tree without branches, then the result would be the same as it in version 1.
• else, the result would be the same as (()(A)(B)((C))D) in version 1. There is an extra bracket on C.
• A paradox will output (BD).
• The form of a printing is ((())(A)B), of which it prints a Unicode character of number of brackets in A.
• that makes it compatible with other languages

## Miscellaneous

This language is uncomputable because obvious.

This language was inspired by SKIΩ calculus and it is supposed to have strength comparable to Xi_2 function.